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Optical excitation and detection of spin precession

M Mehring, Gerhard Wäckerle, Stephan Appelt

Published Aug 27, 1992• 0 citations
Publisher

Abstract

Abstract Soon after the discovery of the principal phenomenon of nuclear magnetic resonance (NMR) by Purcellet al.[1] and Blochet al.[2] , it was Hahn [ 3] who realized that spin precession can be observed directly in the rotating frame as a transient phenomenon called free induction decay (FID). In linear response theory, both phenomena, the continuous wave (c.w.) observation and the free precession are related to each other by Fourier transformation. Within the same year, however, Hahn realized that there is more to the motion of spins than just a linear response to radiofrequency field excitation and discovered the spin echo phenomenon [ 4] which led to the foundation of modern NMR spectroscopy and nonlinear optical spectroscopy. In this contribution we want to present a special view on how these early principles of Hahn influenced the development of Optical Excitation and Detection of Spin Precession. For this purpose we consider a very simple physical system, namely an atomic vapour. In optical pumping spectroscopy it is well known that the transmitted light intensity is modulated by irradiating the system with resonant radiofrequency (r.f.) fields [5-8]. By monitoring the transmission of light as a function of the r.f., sublevel splittings of the optically connected states can thus be measured, which are usually not resolved in the Dopplerbroadened optical spectrum.

DOI
10.1093/oso/9780198539629.003.0021

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Abstract Soon after the discovery of the principal phenomenon of nuclear magnetic resonance (NMR) by Purcellet al.[1] and Blochet al.[2] , it was Hahn [ 3] who realized that spin precession can be observed directly in the rotating frame as a transient phenomenon called free induction decay (FID). In linear response theory, both phenomena, the continuous wave (c.w.) observation and the free precession are related to each other by Fourier transformation. Within the same year, however, Hahn realized that there is more to the motion of spins than just a linear response to radiofrequency field excitation and discovered the spin echo phenomenon [ 4] which led to the foundation of modern NMR spectroscopy and nonlinear optical spectroscopy. In this contribution we want to present a special view on how these early principles of Hahn influenced the development of Optical Excitation and Detection of Spin Precession. For this purpose we consider a very simple physical system, namely an atomic vapour. In optical pumping spectroscopy it is well known that the transmitted light intensity is modulated by irradiating the system with resonant radiofrequency (r.f.) fields [5-8]. By monitoring the transmission of light as a function of the r.f., sublevel splittings of the optically connected states can thus be measured, which are usually not resolved in the Dopplerbroadened optical spectrum.
Abstract The spin echo [1 ] discovered by Erwin Hahn in 1950 is one of the most sophisticated phenomena in physics. It demonstrates the fact that the decay of coherence due to the inhomogeneous broadening can be recovered by an ingenious ‘effective time reversal’ technique. Since then, the research on coherent transients has been developed in the field of pulsed magnetic resonance [2]. The advent of the laser stimulated the studies in the optical region. Optical analogues of most of the coherent transients in magnetic resonance have been realized [ 3] except for those in solids, whose mechanisms are based on the spin temperature hypothesis [4] . Thus coherent interactions between radiation and atoms have been extensively studied and the techniques developed have been effectively used in a variety of fields. In the studies of so-called two-level problems the coherence is generated by a direct excitation of the relevant transitions by radiofrequency (r.f.), microwave, or laser fields.
The dynamics of nuclear spins in atomic and molecular environments have been examined in exquisite detail over the past 27 years by the methods of pulsed nuclear magnetic resonance. The early discovery of the spin echo by Erwin Hahn and the transient nutation effect by Henry Torrey initiated the field by introducing coherent transient phenomena to radio-frequency spectroscopy. An entire class of coherent spin transients could be observed by a simple variation of the rf pulse sequence, and from the decay characteristics the various spin-dephasing mechanisms could be examined separately. In short, these methods allowed decomposition of the spin-transition linewidth into its broadening components, and also offered new and versatile ways for performing high-resolution rf spectroscopy.
Introduction Soon after the development of optical magnetometers based on the radio-optical double resonance method (see Chapter 4), it was realized by Bell and Bloom [1] that an alternative method for optical magnetometry was to modulate the light used for optical pumping at a frequency resonant with the Larmor precession of atomic spins. In a Bell-Bloom optical magnetometer, circularly polarized light resonant with an atomic transition propagates through an atomic vapor along a direction transverse to a magnetic field B . Atomic spins immersed in B precess at the Larmor frequency Ω L , and when the light intensity is modulated at Ω m = Ω L , a resonance in the transmitted light intensity is observed. The essential ideas of the Bell–Bloom optical magnetometer are reviewed in Chapter 1 (Section 1.2), and can be summarized in terms of what Bell and Bloom termed optically driven spin precession: in analogy with a driven harmonic oscillator, in a magnetic field B atomic spins precess at a natural frequency equal to Ω L and the light acts as a driving force oscillating at the modulation frequency Ω m . From another point of view, the Bell-Bloom optical magnetometer can be described in terms of synchronous optical pumping: when Ω m = Ω L , there is a “stroboscopic” resonance in which atoms are optically pumped into a spin state stationary in the frame rotating with Ω L . Depending on the details of the atomic structure, the spin state stationary in the rotating frame can be either a dark state that does not interact with the modulated light or a bright state for which the strength of the light–atom interaction is increased.
Large-amplitude oscillations are predicted in the free-induction decay (FID) of atomic or spin two-level quantum systems that are coherently prepared by a resonant electromagnetic field in the form of a square amplitude pulse of duration TTT. The effect should be detectable in nuclear magnetic resonance (NMR) or in optical resonance experiments when the transition line shape is inhomogeneously broadened (${T}_{2}^{*}\ensuremath{\ll}{T}_{2}$) and the applied field is intense enough that the pulse area $\ensuremath{\chi}T\ensuremath{\ge}2\ensuremath{\pi}$, where $\ensuremath{\chi}$ is the Rabi frequency. Physically, the effect is due to Rabi oscillations which are generated in the preparative stage and are then reproduced because of atomic memory in the radiative period which follows. The atomic polarization derived from the Bloch equations assumes the form of an integral over the inhomogeneous line shape, and can be evaluated numerically for arbitrary linewidth $\ensuremath{\sigma}$ or analytically when $\ensuremath{\sigma}\ensuremath{\rightarrow}\ensuremath{\infty}$. The characteristics of the oscillation are unusual since the oscillation frequency, which is of order $\ensuremath{\chi}$, increases with time while the oscillation envelope vanishes identically for times $t\ensuremath{\ge}2T$. Coherent emission is therefore confined to one pulse width TTT immediately following the pulse. Previous NMR and infrared FID experiments with small-area pulses ($\ensuremath{\chi}T\ensuremath{\le}4\ensuremath{\pi}$), interpreted erroneously in terms of an edge echo effect, support the oscillatory FID behavior described here. For the case $\ensuremath{\chi}T>4\ensuremath{\pi}$, an experimental test would be even more decisive, as the oscillations are more pronounced.
Spin decoupling and line narrowing are observed for the first time in an opticaltransition, 3H4elDZ of Pr3~ in LaF 3 at zOK, using optical FID. The 19F nuclei, when irradiated by an appropriate rf field, undergo forced precession about an effective field at the magic angle in the rotating frame. The fluctuating 19F_19F dipolar interaction is thereby quenched and the optical linewidth drops from -10 to - Z kHz, as predicted in a theory of spin diffusion. In the field of nuclear magnetic resonance (NMR) , there exist several ways of reducing the time-dependent magnetic dipolar interaction between spins. Examples are motional narrowing (l,Z), macroscopic sampIe rotation (3), spontaneous spin flip-flop processes (4), and forced spin precession (5-10). In this article, we report the first observation of this kind in an optical transition of a low temperature solid, LaF 3:Pr 3+, where the dilute nuclear spin (I) is praseodymium and the abundant spin (S) is fluorine. The Pr 3+ ions are coherently prepared by a laser field and thereafter exhibit nonlinear optical free induction decay (FID). The Pr3+ dephasing time, as suggested in earlier work (11), is limited by spin diffusion among the 19F nuclei which undergo resonant flip-flops and impress weak fluctuating fields on the l4lpr nuclei. This action adiabatically modulates the Pr 3+ optical transition frequency through the dipolar I-S interaction and broadens the line. We now show that the half-width half-maximum (HWHM) optical linewidth is reduced from -10 to - Z kHz when the fluorine spin diffusion process is quenched by application of suitable magnetic static snd rf fields, causing the 19F nuclei to precess about an effective magnetic field at the magie angle in the rotating frame. This observation enables us to identify in an unambiguous way that the 19F_19F dipolar interaction is the dominant optical line broadening mechanism and provides the first test of spin diffusion theory' in an optical transition. As we shall see, the behavior at optical and rf frequencies is different. 3+
We report theoretical and experimental studies of the propagation of a square-modulated laser pulse through a laser-cooled atomic ensemble of two-level absorbers, as well as through a three-level system with electromagnetically induced transparency. We find that the transmission characteristics over a wide range of optical depth can be fully accounted for as optical coherent transients excited by the wide spectral content of the square-modulated optical pulse. We show that both time-domain atom-field coupled equations and frequency-domain linear dispersion theory give precisely the same description of the optical transients at a weak power limit. At low optical depth with moderate absorption, resonant excitation dominates and free-induction decay (FID) contributes mostly to the transient field. At high optical depth when absorption and propagation effects become significant, lossless optical precursors start to dominate the transient response. By varying the optical depth from 0 to 45, we observe that optical transients evolve gradually from FID to optical precursors. We thus show that FID and optical precursors, which have been considered as two different optical transients for many decades, can be unified within a single theoretical frame and they are the manifestations of the same physical process in two different regimes.